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A linear stability analysis is performed for the onset of triple-diffusive convection in the presence of internal heat source in a Maxwell fluid saturated porous layer. The layer is considered to be heated and soluted from below. The porous medium is taken as isotropic and homogeneous. Within the framework of linear stability theory and normal made technique, a dispersion relation is obtained. Stationary Rayleigh number and Oscillatory Rayleigh numbers for the onset of instability is determined numerically and results are depicted graphically. The sufficient conditions for the non-existence of overstability are also derived. It has been found that Lewis numbers have destabilizing effect while the solute Rayleigh numbers play stabilizing role. Keywords: Triple-diffusive convection, Maxwell fluid, Internal heat source, Porous medium, Solute gradients